Abstract
In this study we investigate the process of wind-wave generation by using direct numerical simulation (DNS). Air and water domains are respectively solved by Navier-Stokes equations in 3D Cartesian coordinates in which air-water coupled boundary conditions are specified at interface. A shear wind on the top of the air domain is specified, and air and water domains are subsequently driven to fully-developed turbulence, allowing wave growth at interface. In this paper we improve the work published by Lin et al. (2008). Instead of simplified linear boundary conditions (BCs), we derive and impose the non-linear BCs for normal stress at interface, as well as non-linear curvature terms used to balance the discontinuity. The results show that at the linear (initial) stage, faster wave growth is seen with non-linear BCs than with linearized BCs. This is reversed during the exponential (developed) stage.References
Chalikov, D,V. (1978): The numerical simulation of wind-wave interaction, Journal of Fluid Mechanics, 87, 561-582.
Lin, M.-Y., Moeng, C.-H., Tsai, W.-T., Sullivan, P.P., and Belcher, S.E. (2008): Direct numerical simulation of wind-wave generation processes, Journal of Fluid Mechanics, 616, 1-30.
Komen, G. J., L. Cavaleri, M. A. Donelan, K. Hasselmann, S. Hasselmann, and P. A. E. M. Janssen, Eds. (1994): Dynamics and Modelling of Ocean Waves, Cambridge University Press.
Yang, D., Shen, L. (2011a): Simulation of viscous flows with undulatory boundaries. Part I: Basic solver, Journal of Computational Physics, 230, 5488-5509.
Yang, D., Shen, L. (2011b): Simulation of viscous flows with undulatory boundaries: Part II. Coupling with other solvers for two-fluid computations, Journal of Computational Physics, 230, 5510-5531.
Jereys, H. 1925 On the formation of water waves by wind. Proc. R. Soc. Lond. A 107, 189-206.
Phillips, O. M. 1957 On the generation of waves by a turbulent wind. J. Fluid Mech. 2, 417-445.
Phillips, O. M. 1977 Dynamics of the Upper Ocean. Cambridge University Press.
Miles, J. W. 1957 On the generation of surface waves by shear flows. J. Fluid Mech. 3, 185-204.
Belcher, S. E. and Hunt, J. C. R. 1993 Turbulent shear flow over slowly moving waves. J. Fluid Mech. 251, 109-148.